President Obama entrusted oversight of the five Taliban thugs he traded for POW Bowe Bergdahl to the Persian Gulf emirate of Qatar — despite a recent damning US government report that shows terrorists are operating with impunity there, The Post has learned.

The January briefing paper by the nonpartisan Congressional Research Service was drafted to educate lawmakers on the tiny emirate, which hosts several key US military bases but whose monarchy also founded the controversial Al Jazeera news network.

The report highlights the Qatari government’s ties to leaders of the Hamas terror group, noting that Hamas political chief Khaled Meshaal “continues to operate in [Qatar’s capital] Doha after decamping there from Damascus in 2012.”

Israel once tried to assassinate Meshaal for overseeing a wave of suicide bombings that killed dozens of innocent victims and injured hundreds more.

In addition, “Yusuf al Qaradawi, an outspoken Egypt-born religious cleric, also continues to operate in Qatar, where he advocates support for armed Islamist groups in Syria and encourages Egyptians to rise up against the current government, which has sought his arrest,” the report says.

Al Qaradawi, a member of the radical Muslim Brotherhood, has also supported attacks on American forces in Iraq and has been banned from entering the United States since 1999 for his extremist rants.

The 14-page CRS report says recent US concerns about Qatar “have focused on support provided by some Qataris to extremist and terrorist groups abroad.”

“The State Department reported in 2011 that Qatari authorities ‘did not adequately enforce its laws and international standards to track funds transfers to individuals and organizations (including charities) associated with extremists and terrorist facilitators outside Qatar,’ ” according to the CRS.

Specifically mentioned is Abdelrahman bin Umayr al Nuyami, an al Qaeda financier and one of two Qataris the United States last year branded “specially designated global terrorists.”

According to the Treasury Department, Nuyami last year “ordered the transfer of nearly $600,000 to al Qaeda via al Qaeda’s representative in Syria . . . and intended to transfer nearly $50,000 more.”

Nuyami has also “facilitated significant financial support to al Qaeda in Iraq,” the Treasury Department said.

The report also notes that a member of the Qatari royal family, former interior minister Shaykh Abdullah bin Khalid Al Thani, provided support to al Qaeda figures, including Sept. 11 mastermind Khalid Sheik Mohammed.

Qatar’s “counterterrorism cooperation” has improved since then, but as recently as 2011, the State Department said, American officials wanted better “cooperation and information sharing” from the Qataris, the CRS said.

Under the deal that freed Bergdahl, the five Taliban commanders are supposed to live in Qatar for a year.

Obama said their release “was conditioned on the Qataris keeping eyes on them and creating a structure in which we can monitor their activities” — while also admitting there’s “absolutely” a chance they could take up arms against America again.

A senior-level Persian Gulf official has told Reuters that the men are free to move around Qatar, will not be treated as prisoners and no US officials will be involved in monitoring their movements.

In 2008, the US transferred a Gitmo detainee to Qatar with assurances he’d be barred from leaving the country, but he was able to fly to Britain twice before being arrested and deported.